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Monday, January 16, 2012

The ISW mystery I: Introduction

Looks nice Roger, but what are the industrial applications?

Making
science a spectator sport

A
huge part of the motivation for us starting this blog, if not the
main motivation was to present
new research as it is being done.
In other words, to present the view of new research from the very trenches where the discoveries are made. I still intend
(at some point in that mythical, utopian, land called later)
to write a more thorough “motivation for the blog” post; however, the main motivation for presenting new research now, rather than
waiting for Brian Cox to make a documentary about it, is this: it allows everyone
in society to feel involved in scientific research. The hope is that science will then go beyond being just what those guys with beards in
white coats do that we,
everyone else, don't understand and instead becomes something that
society as a whole gets behind and becomes fascinated by and talks
about excitedly during their lunch-break.

You might think this is over-ambitious (though
possibly not if you're reading this blog). But, meh, I think you are
wrong. The public response to scientific discoveries/announcements
last year like this and this tells me that people do care and are
immensely fascinated by what scientists do. If society is not talking
about science at the water-cooler it is because we, the scientists,
are not collectively trying hard enough to involve society in
science. There are numeroushard working and successful exceptionsof course. The fact that they are exceptions is the problem.

Some
scientists reading this might wonder why we even want society talking
about science at the water-cooler. Mightn't science
become corrupted by such base chatter? Think about this again the
next time you are applying for some grant money and have to bend over
backwards trying to come up with possible industrial applications for
your work. Especially when later that evening you could watch a
sportsman get paid millions for doing what he or she chooses to do. I doubt
Nike have ever asked Roger Federer to come up with potential
industrial applications for his backhand. Sportsmen are paid simply
because people like watching them play and think they are cool. But
people also want to
keep track of scientific progress and they definitely also think it
is cool. This latent popularity isn't a bad thing and it isn't being
utilised enough by science.

In this sense this blog, and others like it,
could be described as attempts by scientists to start making science a
spectator sport. Hopefully we'll get better with time.

So, with that unnecessarily long introduction
out of the way, let me finally (from the perspective of both this
post and the blog itself) start telling you about some of my own
research...

I will explain this research through a series of posts (unknown now in number). These posts will be about a mystery. Something that in the title to this post I have called the ISW mystery. At the moment, nobody knows the answer to the ISW mystery. It is a new mystery. It first became apparent as recently as 2008 and although the problem is better understood now than then it still remains a mystery. My contributions towards solving the ISW mystery started last year.

It is highly possible that by the time I'm finished with this series of posts it won't be a mystery anymore (maybe my collaborators and I will have solved it, maybe we'll get scooped). In any case, this is it, the frontier of research. I don't know the final destination of this any better than you do!

Your humble writer, standing on the metaphorical edge of human
knowledge, more than a little terrified about what lies beyond.

What
I have only vaguely alluded to so far is the 13.7 billion year
journey taken by the CMB's light between its creation and its
detection. There is a habit of cosmologists to view this journey as
uninteresting and anything that happens during it as a nuisance. This
is partially well-motivated. The CMB, when formed, was an almost
perfect image of the state of the early universe. Anything that
happened to it afterwards will have corrupted what could otherwise have been an
ideal photograph. However, it is ultimately foolish because in these
secondary effects there is much that we can determine about the
evolving universe. The CMB is the one thing we can currently measure
in the universe that is literally everywhere. At every
single cosmological event since it was formed the CMB was
there, watching. So, if we are clever enough, and the CMB interacted
somehow with an event, we can use the CMB to learn things about it.
We may even learn things about events that would otherwise be
completely impossible to actually see.

In
other words these secondary effects aren't nuisances, they're just a
different type of mineral in the amazing CMB quarry.

I
am going to be writing in this series of posts about the effects of
gravity on the CMB. This is because it appears
that certain gravitational effects on the CMB from enormously large
structures in the universe are much, much, larger than we expect (i.e. the ISW mystery). Why
this anomaly exists, nobody yet knows. It could be that it is an indication that some sort of adaptation is needed to general
relativity, which gives us the laws of gravity. It could be that the
sizes of the largest structures in the universe are much bigger than
we expect. This would indicate that the initial fluctuations of the
universe do not follow the distribution that our simplest models
predict (and that work everywhere else). Either of these results
would have huge implications for our knowledge of fundamental
physics.

Alternatively,
this anomaly could be evidence that some seemingly obvious
assumptions being made in cosmological calculations are wrong. There
are even candidates for what these assumptions might be. This might
sound like the most likely possible explanation (and also the least
interesting). However, it is actually the most messy potential
explanation of them all. These assumptions are widespread in our cosmological
calculations and, mostly, they seem to work very well. Any proof that
they are wrong (and they may be
wrong) would have dramatic consequences to our understanding
of the evolution of the universe. This in turn could have dramatic
consequences for the interpretations we've made about fundamental
physics based on that understanding.

Or,
finally, the anomalously large signal could be a statistical fluke.
The chances of this are less than 1 in 1000, so very unlikely, but
not impossibly unlikely. Chance may just be playing a cruel trick on
us – it is possible!

Whatever
the explanation for this anomaly is, it will have to change the
anomalous calculation in such a way as to remove the discrepancy
without ruining all the other predictions that the standard
cosmological model got right elsewhere in the universe. This is no
simple task and each of the possibilities I listed above, except for
the statistical fluke, comes with baggage concerning other
measurable quantities. Really, this just makes this anomaly (and any
others) all that much more intriguing. Is it really telling us that
something is wrong with our understanding of the fundamental aspects
of the universe? And if so... what?

How
does gravity affect the CMB?

There
is structure in the universe. All through the CMB's journey towards
detection there have been regions of space that are slightly more
dense and regions that are slightly less dense. Gravitationally, all
(ordinary) matter will pull other things towards it. As I've explained before, this means that the more dense regions of space
will pull things towards them slightly more than the less dense
regions.

Light, and thus the CMB, are no exceptions to this pulling. As the CMB has
travelled the universe it has been receiving subtle net pulls towards
over dense regions that pull slightly more than the rest of the
universe and subtle net pushes away from under dense regions that
pull slightly less. This subtle pushing and pulling on light as it
travels past structure is known as gravitational lensing. Lensing is
responsible for small deviations to what would otherwise be a
straight path for the light in the CMB.

Extremely
dense objects, such as galaxy clusters, can actually lens some light
travelling past them so strongly that they act just like an optical
lens would on Earth, producing (for example) multiple images of
something behind them. However, objects dense enough to act like such
a strong lens are rare and small in size. What is more common is
known as weak lensing. Weak lensing merely distorts an image behind
the lensing object. But it can be seen and measured and can be used
to obtain information about the lensing object and the light source
being lensed. Both of these types of lensing are important sources of
knowledge in cosmology. However it isn't only lensing that affects
the CMB gravitationally and it isn't lensing that I will be
discussing in these posts (not for a while at least).

Some pretty intense gravitational lensing going on around a galaxy.
(The blue horseshoe is a galaxy lensed by the red galaxy at the centre of the image)

When
matter is pulled by other matter it doesn't just change path it can
also speed up or slow down. This speeding up or slowing down results
in changes in the energy of the matter being pulled. Unlike matter, light can't change its speed. That is constant. But it can
change energy, and does (remember that different energy light
has a different wavelength/frequency/colour). When light falls
towards an attractive region of higher density, it gains energy. When
it climbs out of such a region it loses energy. Conversely, when it
climbs into a net repulsive region of lower density it loses energy
and when it falls out of such a region it gains energy. For the CMB, any gain or loss in energy corresponds directly to a gain or loss in
temperature. With luck (for me) this won't be new to readers of this
blog because it is also this phenomenon that (partially) generates
the initial fluctuations in the CMB temperature as it climbs (or
falls) out of the density fluctuations it was formed in (as I explained earlier).

Therefore,
as the CMB travels through the universe it is constantly climbing in and out
of gravitational wells and hills, gaining and losing energy as it
goes. The miracle is... very nearly, none of this matters. To
understand why, first consider the CMB's light travelling through a
perfectly stationary universe. Even in this hypothetical world there
would still be gravitational wells and hills, but none of this would
matter. The reason is that no matter how deep into a well any part of the CMB
fell, or how high up a hill it got, we know it must come
back out of the structure if we are to detect it at Earth! Therefore, if we are
following the CMB from origin to detection, if we want to know the net change in its temperature/energy we don't need to know anything
about what path it took to get here. All we need to know is how far
up or down a well or hill it was when created and how far up or down
a hill we are here. Turning that around, if we can measure the
temperature fluctuations of the CMB here at Earth, then we are
directly measuring the density perturbations where the CMB was formed
13.7 billion years ago.

But
wait, the universe is not stationary. In fact, in the real universe, the density perturbations are actually always growing with time.

Surely
this means that the gravitational wells and hills are growing too?

In fact, it
doesn't and here is why...

The
universe is also expanding!

Because
the universe is expanding, even though (everywhere) the fluctuations
in density are growing, they are also getting further apart (almost
everywhere). The energy gained or lost by light (or anything else) as
it travels past any matter in the universe depends both on how much mass the matter has and how close the light gets to the
matter. In our expanding universe with ever growing structures these
effects almost completely cancel out.

Two
things conspire to stop them cancelling perfectly. These are dark energy and (writing a
bit loosely) gravitational instability. Dark energy stops the effects cancelling by providing a push that increases the expansion rate of the universe. This means that structures in the universe move apart at a faster rate than the rate at which they gain more mass. This causes
the gravitational wells and hills to shrink late in the universe's
history when dark energy starts to work its magic. Gravitational
instability causes structures to start to form more quickly,
(probably) without also causing the universe to expand faster. This
causes the gravitational wells and hills to grow late in the
universe's history. Any parts of the CMB that are caught in a well or
hill while the well or hill changes size will experience a net shift
in temperature. This is simple to see. If a well was deeper when
light fell into it than when the light climbed out of it, then there
will be a net increase in the light's energy/temperature from
traversing the well. If the well was shallower, there will be a net
decrease in the light's energy/temperature. The converse holds for
hills.

This
net temperature shift in the CMB is called the integrated Sachs-Wolfe
(ISW) effect. This name comes from the Sachs-Wolfe effect which is
applied to the simple gain and loss of energy as light falls in and
out of gravitational wells (that name came about in the obvious
manner). It is this ISW effect that seems to have been measured and appears to be much larger than expected.

How it has (probably) been measured and how we know how big the signal should be will come in later posts... (now continued here)

4 comments:

I find it interesting that you say 'at Earth' rather than 'on Earth', which would be the usual convention. I suppose that if you're always considering the Earth in the wider context of the Universe then 'at' would be more appropriate.

Hah, yes I made a conscious decision about that. I did originally write "on Earth". The reason why I changed actually has nothing to do with the universe in a wider context. Two of the CMB detectors (COBE and WMAP) have been space based satellites (with a third, Planck, still to report) and many have been balloon based. So quite literally, "on Earth" just didn't feel right to me.

Trying to understand ISW as it pertains to law of conservation of energy - if light exits a gravity well with a different energy to when it went in, how do we account for the difference? Is it drawn from or deposited with the massive body responsible for the gravitational field? What form does this energy take? In a different context, I guess I'm asking if a photon can minutely affect the kinetic energy of a planet!

Firstly, yes a photon definitely does minutely affect the kinetic energy of a planet. In general relativity it is energy that causes gravitational forces, not mass. Mass of course does also gravitate, but only because it carries energy. So, because any photon carries energy it also pushes and pulls anything else that is affected by gravity.

But more surprisingly, in general relativity, energy is not actually conserved. Or, at least, the energy of all the matter and radiation in the universe is not conserved. This is somewhat obvious when you realise that dark energy is a field of constant energy *density*, no matter what volume it is put in. So, even when the universe doubles in volume, the *density* of dark energy remains the same, which means that as the universe expands the total energy in the dark energy field is constantly increasing. This post at the Cosmic Variance blog explains the issue of energy conservation in general relativity quite well.

The point is that, even though the photon is exchanging energy with the matter as it falls in and out of the gravitational wells, the fact that there is a net gain or loss of energy in the photon doesn't necessarily require that there is a net loss or gain of energy in the matter to compensate. It is precisely the uncompensated decay in the gravitational potential of the matter that allows for there to be a net effect on the photon.

I hope that helps. If it isn't clear, feel free to ask for clarification. And you should definitely read through the link to Cosmic Variance that I provided.